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If x^(y) . Y^(x) =16 " then " (dy)/(dx) ...

If` x^(y) . Y^(x) =16 " then " (dy)/(dx) " at" (2,2)` is equal to

A

`-1`

B

0

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`ylog_e x + xlog_e y = 4log_e2`
Now, differentiating both side w.r.t. x
`y/x + log_e x (dy)/(dx)+x/y (dy)/(dx) + log_e y.1=0 rArr (dy)/(dx)=-((log_e y+y/x))/((log_e x + x/y))`
`rArr ((dy)/(dx))"|"_"(2,2)"=-((log_e 2+1))/((log_e 2+1))=-1`
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